The Gunners under Wenger have built a reputation for buying younger players on lesser wages and then developing them before selling them on.
But speaking to Al Jazeera, Wenger has hinted that for Rooney he's prepared to make an exception.
"Rooney could be an interesting player for everybody in the world," Wenger said. "Who would turn him down?
"David Moyes' first challenge is to go in to Manchester United and if Rooney bears a grudge or not, we will see. It will be interesting to see how that will be handled."
It's still a big stretch to see Rooney at the Emirates, however - even if Arsenal shatter their wage policy as the Mail suggests and offer a deal over five years with £170,000-a-week wages, it would still be a reduction on the reported £250k Rooney picks up weekly at Old Trafford.
Far more realistic, it would seem, is the interest in Swansea striker Michu.
More than the big names, such as Rooney, Gonzalo Higuain and Stevan Jovetic, Michu fits the Arsenal mould, and the Mail says the deal has already been discussed with the scouting team at the Emirates.
Michu would cost significantly more than the £2m Swansea spent on him less than a year ago, but at 27 could still represent value and proven Premier League quality.
Also on the shopping list is Michu's captain at the Liberty Stadium, Ashley Williams.
Wenger may need a new centre-half, according to The Sun, because Bayern Munich are prepared to offer £15m for the signature of Laurent Koscielny, who impressed last season.
Want to know who Jose Mourinho's first signing as Chelsea boss will be? So does everyone else - but this effort in The Sun seems a bit fanciful. The paper suggests that Wesley Sneijder could move to Stamford Bridge, and they base their report on sources in Turkey.
While Mourinho and Sneijder are said to get on famously from their time at Internazionale, with the likes of Juan Mata, Oscar and Eden Hazard in those playmaker positions it is hard to see where Sneijder could fit in.
Elsewhere The Guardian carry an interesting report linking Liverpool to a £22m-rated Armenian striker.
Henrikh Mkhitaryan bagged 25 goals for Shakhtar Donetsk last season, and the 24-year-old has been linked to a move to a major European club this summer.
According to the paper, the Reds are prepared to back Brendan Rodgers on the move irrespective of whether Luis Suarez leaves the club.
Rodgers' preferred choice of new centre-half is Kyriakos Papadopoulos of Schalke, but there is a disagreement over his valuation. The Bundesliga club are holding out for closer to £20m, while Liverpool are prepared to spend more like £12m for him.
David Villa has put off suitors for the time being by saying he will not make any decisions over his future until the end of the Confederations Cup.
The Barcelona and Spain striker is in South America for the tournament which runs from June 15-30, and will only let the likes of Tottenham and Arsenal know his plans once his season is over.
One man seemingly sure to move is Netherlands keeper Maarten Stekelenburg. Fulham are expected to wrap up a £3m move for the Roma stopper this week (Daily Express).
Fellow keeper Asmir Begovic of Stoke is to hold discussions with the club over his future, with Liverpool, Manchester United, Chelsea and Arsenal all having shown recent interest in him (Daily Star).
And in a final piece of Premier League news, despite the notes of caution from Goodison Park last night, almost all the papers expect Roberto Martinez to be confirmed as the new Everton manager later today.